Abstract We consider the critical spread-out contact process in Z with d ≥ 1, whose infection range is denoted by L ≥ 1. The two-point function τt(x) is the probability that x ∈ Z is infected at time t by the infected individual located at the origin o ∈ Z at time 0. We prove Gaussian behavior for the two-point function with L ≥ L0 for some finite L0 = L0(d) for d > 4. When d ≤ 4, we also perfo...

This file provide the detailed steps for obtaining the bounds on R1, R2 via the obtained results on (R1c, R1p, R2c, R2p). The rate pair (R1c, R1p, R2c, R2p) is achievable if it satisfies following inequalities. R1c ≤ rank(U 1 H11V21) (1) R1p ≤ m1 − r21 (2) R2c ≤ r12 (3) R1c +R1p ≤ r11 (4) R1c +R2c ≤ r12 + rank(U 10H11V21) (5) R1p +R2c ≤ r12 + rank(U 10H11V20) (6) R1c +R1p +R2c ≤ n1 (7) R2c ≤ ra...

We present modifications of model elimination which do not necessitate the use of contrapositives. These restart model elimination calculi are proven sound and complete. The corresponding proof procedures are evaluated by a number of runtime experiments and they are compared to other well known provers. Finally we relate our results to other calculi, namely the connection method, modified probl...

The generalized Higham matrix is a complex symmetric matrix A = B + iC, where both B ∈ Cn×n and C ∈ Cn×n are Hermitian positive definite, and i = √−1 is the imaginary unit. The growth factor in Gaussian elimination is less than 3 √ 2 for this kind of matrices. In this paper, we give a new brief proof on this result by different techniques, which can be understood very easily, and obtain some ne...

We solve the Kato problem for divergence form elliptic operators whose heat kernels satisfy a pointwise Gaussian upper bound. More precisely, given the Gaussian hypothesis, we establish that the domain of the square root of a complex uniformly elliptic operator L = −div(A∇) with bounded measurable coefficients in Rn is the Sobolev space H1(Rn) in any dimension with the estimate ‖ √ Lf‖2 ∼ ‖∇f‖2...

selective harmonic elimination (she) is a powerful modulation scheme aims to find the required switching angles in order to eliminate the number of undesired harmonics. she is a complicated problem which consists of several nonlinear equations which have multiple local minima. in order to eliminate the higher number of undesired harmonics and as a result reducing the total harmonic distortion (...